Question

Two cards are drawn successively from an ordinary deck of 52 well-shuffled cards. Find the probability that a. the first card is not

a Four of Clubs or an Five;

b. the first card is an King but the second is not;

c. at least one card is a Spade;

Answer 1

a) Probability that the first card id not four of clubs or a five is computed here as:

= (Number of cards which are neither four of clubs nor 5 ) / Total cards

= (52 - 1 - 4) / 52

= 47/52

= 0.9038

Therefore 0.9038 is the required probability here.

b) Probability that the first card is a king and second is not is computed here as:

= Probability that the first card is a king * Probability that the second card is not a king given that 1 king has already been taken out

= (4/52)*(48/51)

= 0.0724

Therefore 0.0724 is the required probability here.

c) Probability that at least one card is a spade is computed here as:

= 1 - Probability that none of the spades is taken out

= 1 - (Number of ways to take out 2 non spade cards / Number of ways to select 2 cards from 52 cards)

Therefore 0.4412 is the required probability here.